Periodic solutions of forced Kirchhoff equations

Baldi, Pietro

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 5, Tome 8 (2009) no. 1, pp. 117-141.

We consider the Kirchhoff equation for a vibrating body, in any dimension, in the presence of a time-periodic external forcing with period $2\pi /\omega$ and amplitude $\epsilon$. We treat both Dirichlet and space-periodic boundary conditions, and both analytic and Sobolev regularity. We prove the existence, regularity and local uniqueness of time-periodic solutions, using a Nash-Moser iteration scheme. The results hold for parameters $(\omega ,\epsilon )$ in a Cantor set with asymptotically full measure as $\epsilon \to 0$.

Classification : 35L70, 45K05, 35B10, 37K55

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